Question

an official for a regional baseball league examines attendance data for teams in the league. for each team in the league, the number of losses and the average game attendance is shown in the scatterplot. the value of r for the scatterplot is -0.847. which of these data combinations weakens the correlation? 2 losses, 11.9 thousand fans 2 losses, 15.2 thousand fans 5 losses, 10.3 thousand fans 9 losses, 7.7 thousand fans

Explanation:

A strong negative correlation (\(r = - 0.847\)) means that as the number of losses increases, the average game attendance decreases. To weaken the correlation, we need a data - point that does not follow this trend.

• For the data - point \(2\) losses, \(11.9\) thousand fans: Looking at the scatter - plot, when the number of losses is low (around \(0 - 5\)), the average attendance is relatively high. A value of \(11.9\) thousand fans for \(2\) losses is in line with the general trend (high attendance for low losses).
• For the data - point \(2\) losses, \(15.2\) thousand fans: This is an outlier. The general trend for low losses (e.g., near \(0 - 5\) losses) has average attendances in the range of \(10 - 15\) thousand, but \(15.2\) is at the upper - end of what would be expected for the general negative trend. It is less in line with the overall negative correlation pattern compared to the other non - outlier points.
• For the data - point \(5\) losses, \(10.3\) thousand fans: When the number of losses is around \(5\), looking at the scatter - plot, the average attendance is in the range where we would expect for a negative correlation (lower than the attendance for \(0 - 2\) losses).
• For the data - point \(9\) losses, \(7.7\) thousand fans: When the number of losses is around \(9\), according to the negative correlation (more losses, less attendance), this value is in line with the general trend.

Answer:

2 losses, 15.2 thousand fans